1. The problem asks us to explain the function $f(a+3) = (a+3)^2$. 2. This function represents the square of the expression $a+3$. 3. To understand it better, we expand the square using the algebraic identity $ (x+y)^2 = x^2 + 2xy + y^2 $. 4. Here, $x = a$ and $y = 3$, so: $$ (a+3)^2 = a^2 + 2\cdot a \cdot 3 + 3^2 = a^2 + 6a + 9 $$ 5. This means the function $f(a+3)$ takes an input $a$, adds 3 to it, and then squares the result. 6. The output is a quadratic expression in $a$ given by $a^2 + 6a + 9$. 7. This helps to understand how changes in $a$ affect the value of $f(a+3)$ since it's a parabola opening upwards with vertex at $a = -3$. 8. In summary, $f(a+3)$ is the square of $a+3$, expanded to $a^2 + 6a + 9$ showing a quadratic pattern.